ScienceMathDefinitionsIntroduction To Proof Assignment And Quiz
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Introduction To Proof Assignment And Quiz

Finnian Jackson avatar Finnian Jackson
7 September 2022
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19 test answers

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question
Which statement is true about the diagram?
answer
∠BEA ≅ ∠BEC
question
Segment AB is congruent to segment AB. This statement shows the _____ property
answer
reflexive
question
Given that RT ≅ WX, which statement must be true?
answer
RT + TW = WX + TW
question
A two-column proof
answer
contains a table with a logical series of statements and reasons that reach a conclusion.
question
Given that D is the midpoint of AB and K is the midpoint of BC, which statement must be true?
answer
AK + BK = AC
question
What is the missing justification?
answer
transitive property
question
Given that ∠CEA is a right angle and EB bisects ∠CEA, which statement must be true?
answer
m∠CEB = 45°
question
Given that ∠ABC ≅ ∠DBE, which statement must be true?
answer
∠ABD ≅ ∠CBE
question
Which statement is true about the diagram?
answer
K is the midpoint of AB.
question
Given that BA bisects ∠DBC, which statement must be true?
answer
m∠ABD = m∠ABC
question
Name the three different types of proofs you saw in this lesson. Give a description of each.
answer
One type of proof is a two-column proof. It contains statements and reasons in columns. Another type is a paragraph proof, in which statements and reasons are written in words. A third type is a flowchart proof, which uses a diagram to show the steps of a proof.
question
Which property is shown? If m∠ABC = m∠CBD, then m∠CBD = m∠ABC
answer
symmetric property
question
EB bisects ∠AEC. What statements are true regarding the given statement and diagram?
answer
∠CED is a right angle. ∠CEA is a right angle. m∠CEB = m∠BEA m∠DEB = 135°
question
Given: m∠ABC = m∠CBD Prove: BC bisects ∠ABD. Justify each step in the flowchart proof.
answer
A: given B: definition of congruent C: definition of bisect
question
Describe the main parts of a proof.
answer
Proofs contain given information and a statement to be proven. You use deductive reasoning to create an argument with justification of steps using theorems, postulates, and definitions. Then you arrive at a conclusion.
question
Given: EB bisects ∠AEC. ∠AED is a straight angle. Prove: m∠AEB = 45° Complete the paragraph proof. We are given that EB bisects ∠AEC. From the diagram, ∠CED is a right angle, which measures __° degrees. Since the measure of a straight angle is 180°, the measure of angle ______ must also be 90° by the _____. A bisector cuts the angle measure in half. m∠AEB is 45°.
answer
90 AEC angle addition postulate
question
Given: ∠ABC is a right angle and ∠DEF is a right angle. Prove: All right angles are congruent by showing that ∠ABC ≅∠DEF. What are the missing reasons in the steps of the proof?
answer
A: definition of right angle B: substitution property C: definition of congruent angles
question
Identify the missing parts in the proof. Given: ∠ABC is a right angle. DB bisects ∠ABC. Prove: m∠CBD = 45°
answer
A: given B: measure of angle ABC = 90 C: angle addition postulate D: 2 times the measure of angle CBD = 90
question
Given: m∠A + m∠B = m∠B + m∠C Prove: m∠C = m∠A Write a paragraph proof to prove the statement.
answer
We are given that the sum of the measures of angles A and B is equal to the sum of the measures of angles B and C. The measure of angle B is equal to itself by the reflexive property, so you can subtract that measure from both sides of the equation. Now the measure of angle A equals the measure of angle C. By the symmetric property, this means the measure of angle C equals the measure of angle A.